A block orthogonal projection algorithm using order recursive UD factorization

Adaptive algorithms for modifying filter coefficients play an important rol e in adaptive signal processing. Various methods have been proposed to date . Of these, the algorithm based on the orthogonal projection into a subspac e spanned by the input signal vector has the property of estimating the opt imum filter coefficients rapidly even if the input signals are correlated. Among the methods based on the orthogonal projection operation, the block o rthogonal projection algorithm is a method that has a good balance between computational complexity and convergence properties. This algorithm is expr essed in terms of a form containing the Moore-Penrose-type generalized inve rse matrix. Several methods have been proposed for specific execution of th is algorithm. In this paper, a lemma on the UD decomposition and the block inverse matrix for the autocorrelation matrix is used for a method executin g the block orthogonal projection algorithm containing a Moore-Penrose-type generalized inverse matrix with less computational complexity than that in the conventional method. The present method is characterized by computatio n of the orthogonal projection matrix corresponding to the i-th step in an arbitrary block by means of the orthogonal projection matrix of the precedi ng step. By computer simulation, the present method and that proposed earli er are compared and the superiority of the present algorithm is discussed. (C) 2000 Scripta Technica.